Production is said to be of the form $u \to v$. I want to know if you distinguish $u$ from $v$ giving them some distinguishing names, like LHS/RHS or something alike.
Yes, I have found it in Parsing techniques: A practical guide
For brevity we write ---> instead of “may be replaced by”; since terminal and non-terminal symbols are now identified as technical objects we shall write them in a typewriter-like typeface. The part before the ---> is called the left-hand side, the part after it the right-hand side.